A variant of the Newton method

Let \(X\) be a Banach space, \(Y\) a normed space, \(P:X\rightarrow Y\) a nonlinear operator and the equation \(P\left( x\right) =0\). The first order derivative is approximated by the partial derivative of an operator of two variables, whose diagonal restrictive coincides with \(P\). We give a semilocal convergence result for the considered method.

Ion Păvăloiu
(Tiberiu Popoviciu Institute of Numerical Analysis)

Original title (in French)

Une variante de la méthode de Newton

English translation of the title

A variant of the Newton method

two step Newton type method; semilocal convergence; nonlinear equation in Banach space

Scanned paper.

I. Păvăloiu, Une variante de la méthode de Newton, Anal. Numér. Théor. Approx., 7 (1978) no. 1, pp. 95-99 (in French).

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